← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 19 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 9900 (c) 4950 (d) 4851
  2. 2.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 48 (b) 510 (c) 255 (d) 280
  3. 3.What is the 29th term of the AP 1, 5, 9, 13, …? (a) 113 (b) 116 (c) 112 (d) 117
  4. 4.What is the 19th term of the AP 6, 8, 10, 12, …? (a) 44 (b) 42 (c) 38 (d) 36
  5. 5.What is the 33rd term of the AP 5, 10, 15, 20, …? (a) 160 (b) 170 (c) 166 (d) 165
  6. 6.What is the missing term in the AP 16, 21, ?, 31, 36? (a) 31 (b) 27 (c) 26 (d) 25
  7. 7.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 17 (b) 114 (c) 66 (d) 57
  8. 8.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 122 (b) 242 (c) 121 (d) 16
  9. 9.What is the missing term in the AP 7, ?, 23, 31, 39? (a) 14 (b) 16 (c) 15 (d) 23
  10. 10.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 230 (b) 225 (c) 45 (d) 450
  11. 11.What is the sum of all the whole numbers from 1 to 38? (a) 1482 (b) 741 (c) 703 (d) 722
  12. 12.What is the 16th term of the AP 10, 12, 14, 16, …? (a) 42 (b) 30 (c) 32 (d) 40
  13. 13.What is the 24th term of the AP 17, 20, 23, 26, …? (a) 89 (b) 72 (c) 86 (d) 69
  14. 14.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 180 (b) 360 (c) 192 (d) 26
  15. 15.What is the 39th term of the AP 11, 14, 17, 20, …? (a) 125 (b) 114 (c) 117 (d) 128
  16. 16.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 200 (b) 370 (c) 185 (d) 32
  17. 17.What is the sum of all the whole numbers from 1 to 68? (a) 2278 (b) 4692 (c) 2312 (d) 2346
  18. 18.What is the 10th term of the AP 17, 23, 29, 35, …? (a) 54 (b) 77 (c) 71 (d) 60
  19. 19.What is the missing term in the AP 6, 15, ?, 33, 42? (a) 23 (b) 24 (c) 33 (d) 25
  20. 20.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 17 (b) 88 (c) 160 (d) 80
  21. 21.What is the 19th term of the AP 13, 17, 21, 25, …? (a) 72 (b) 89 (c) 76 (d) 85
  22. 22.What is the 14th term of the AP 14, 22, 30, 38, …? (a) 126 (b) 104 (c) 112 (d) 118
  23. 23.What is the missing term in the AP 15, ?, 25, 30, 35? (a) 19 (b) 21 (c) 20 (d) 25
  24. 24.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 379 (c) 378 (d) 756
  25. 25.What is the missing term in the AP 19, ?, 25, 28, 31? (a) 21 (b) 23 (c) 25 (d) 22
  26. 26.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 4422 (c) 2211 (d) 2145
  27. 27.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 374 (b) 748 (c) 59 (d) 379
  28. 28.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 245 (b) 490 (c) 47 (d) 270
  29. 29.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 625 (d) 650
  30. 30.What is the 20th term of the AP 4, 10, 16, 22, …? (a) 120 (b) 118 (c) 114 (d) 124
  31. 31.What is the 31st term of the AP 13, 16, 19, 22, …? (a) 93 (b) 103 (c) 106 (d) 90
  32. 32.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 222 (b) 31 (c) 126 (d) 111
  33. 33.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 324 (d) 171
  34. 34.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 100 (c) 19 (d) 110
  35. 35.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 378 (b) 194 (c) 41 (d) 189
  36. 36.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 576 (d) 47
  37. 37.What is the missing term in the AP 5, 12, ?, 26, 33? (a) 18 (b) 26 (c) 19 (d) 20
  38. 38.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 497 (c) 465 (d) 496
  39. 39.What is the 11th term of the AP 7, 16, 25, 34, …? (a) 97 (b) 106 (c) 90 (d) 99
  40. 40.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 75 (b) 150 (c) 12 (d) 80

Answer key

  1. 4950
  2. 255
  3. 113
  4. 42
  5. 165
  6. 26
  7. 57
  8. 121
  9. 15
  10. 225
  11. 741
  12. 40
  13. 86
  14. 180
  15. 125
  16. 185
  17. 2346
  18. 71
  19. 24
  20. 80
  21. 85
  22. 118
  23. 20
  24. 378
  25. 22
  26. 2211
  27. 374
  28. 245
  29. 625
  30. 118
  31. 103
  32. 111
  33. 324
  34. 100
  35. 189
  36. 576
  37. 19
  38. 496
  39. 97
  40. 75

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad